jmp design of experiments

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Design of experiments

What is design of experiments.

Design of experiments (DOE) is a systematic, efficient method that enables scientists and engineers to study the relationship between multiple input variables (aka factors) and key output variables (aka responses). It is a structured approach for collecting data and making discoveries.

When to use DOE?

• To determine whether a factor, or a collection of factors, has an effect on the response.
• To determine whether factors interact in their effect on the response.
• To model the behavior of the response as a function of the factors.
• To optimize the response.

Ronald Fisher first introduced four enduring principles of DOE in 1926: the factorial principle, randomization, replication and blocking. Generating and analyzing these designs relied primarily on hand calculation in the past; until recently practitioners started using computer-generated designs for a more effective and efficient DOE.

Why use DOE?

DOE is useful:

• In driving knowledge of cause and effect between factors.
• To experiment with all factors at the same time.
• To run trials that span the potential experimental region for our factors.
• In enabling us to understand the combined effect of the factors.

To illustrate the importance of DOE, let’s look at what will happen if DOE does NOT exist.

Experiments are likely to be carried out via trial and error or one-factor-at-a-time (OFAT) method.

Trial-and-error method

Test different settings of two factors and see what the resulting yield is.

Say we want to determine the optimal temperature and time settings that will maximize yield through experiments.

How the experiment looks like using trial-and-error method:

1. Conduct a trial at starting values for the two variables and record the yield:

2. Adjust one or both values based on our results:

3. Repeat Step 2 until we think we've found the best set of values:

As you can tell, the  cons of trial-and-error  are:

• Inefficient, unstructured and ad hoc (worst if carried out without subject matter knowledge).
• Unlikely to find the optimum set of conditions across two or more factors.

One factor at a time (OFAT) method

Change the value of the one factor, then measure the response, repeat the process with another factor.

In the same experiment of searching optimal temperature and time to maximize yield, this is how the experiment looks using an OFAT method:

1. Start with temperature: Find the temperature resulting in the highest yield, between 50 and 120 degrees.

    1a. Run a total of eight trials. Each trial increases temperature by 10 degrees (i.e., 50, 60, 70 ... all the way to 120 degrees).

    1b. With time fixed at 20 hours as a controlled variable.

    1c. Measure yield for each batch.

2. Run the second experiment by varying time, to find the optimal value of time (between 4 and 24 hours).

    2a. Run a total of six trials. Each trial increases temperature by 4 hours (i.e., 4, 8, 12… up to 24 hours).

    2b. With temperature fixed at 90 degrees as a controlled variable.

    2c. Measure yield for each batch.

3. After a total of 14 trials, we’ve identified the max yield (86.7%) happens when:

• Temperature is at 90 degrees; Time is at 12 hours.

As you can already tell, OFAT is a more structured approach compared to trial and error.

But there’s one major problem with OFAT : What if the optimal temperature and time settings look more like this?

We would have missed out acquiring the optimal temperature and time settings based on our previous OFAT experiments.

Therefore,  OFAT’s con  is:

• We’re unlikely to find the optimum set of conditions across two or more factors.

How our trial and error and OFAT experiments look:

Notice that none of them has trials conducted at a low temperature and time AND near optimum conditions.

What went wrong in the experiments?

• We didn't simultaneously change the settings of both factors.
• We didn't conduct trials throughout the potential experimental region.

The result was a lack of understanding on the combined effect of the two variables on the response. The two factors did interact in their effect on the response!

A more effective and efficient approach to experimentation is to use statistically designed experiments (DOE).

Apply Full Factorial DOE on the same example

1. Experiment with two factors, each factor with two values. 

These four trials form the corners of the design space:

2. Run all possible combinations of factor levels, in random order to average out effects of lurking variables .

3. (Optional) Replicate entire design by running each treatment twice to find out experimental error :

4. Analyzing the results enable us to build a statistical model that estimates the individual effects (Temperature & Time), and also their interaction.

It enables us to visualize and explore the interaction between the factors. An illustration of what their interaction looks like at temperature = 120; time = 4:

You can visualize, explore your model and find the most desirable settings for your factors using the JMP Prediction Profiler .

Summary: DOE vs. OFAT/Trial-and-Error

• DOE requires fewer trials.
• DOE is more effective in finding the best settings to maximize yield.
• DOE enables us to derive a statistical model to predict results as a function of the two factors and their combined effect.

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Article Contents

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Introduction to Design of Experiments with JMP Examples

• Article contents
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• Supplementary Data

S. E. Lazic, Introduction to Design of Experiments with JMP Examples, Journal of the Royal Statistical Society Series A: Statistics in Society , Volume 173, Issue 3, July 2010, Pages 692–693, https://doi.org/10.1111/j.1467-985X.2010.00646_5.x

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This book is written for practising engineers and researchers, and thus has a very applied focus; it would perhaps be less suitable for a course textbook, since problems and exercises are not included. All the examples are from situations that would be found in an industrial setting, especially manufacturing and production.

The book does a fair job of covering basic concepts and ideas and illustrates the results by using JMP software (from the SAS Institute). The book is not a step-by-step manual showing how to use JMP for the design of experiments, as there is a separation between ‘what to do conceptually’ and ‘how actually to do it in JMP’. Only in the final chapter (which is more like an appendix) are details given regarding implementation.

Regarding the structure of the book, one could question the logic of putting the chapter ‘Statistical concepts for designed experiments’ (Chapter 5) after ‘A three-factor designed experiment’ (Chapter 3) and ‘Four-factor full-factorial experiments’ (Chapter 4). Concepts such as populations versus samples, degrees of freedom and interactions should arguably be introduced before a full factorial analysis.

The style is very ‘choppy’: almost as if a PowerPoint presentation had been made into a book. Many pages contained excessive blank space, partly because of the size of the headings and subheadings, and often there is very little text under either. I was left with the impression that the authors started with a skeleton of topics that they wanted to discuss but did not quite flesh them out. Often there are several consecutive paragraphs that are only a sentence in length, and all relating to the same topic; these could have been combined into a single paragraph and would have made the ideas flow together more smoothly. It is thus not very dense with information and, if the book were to be reformatted in the style of CRC Press or Springer for example, it would be reduced in size by half. There were also many errors in referencing equations (more than expected given that it is the third edition), and values in the figures did not always correspond to values in the text or figure captions.

The book does describe concepts in an intuitive manner, and the chapter on optimal designs (Chapter 11) is particularly good in this regard. However, the topics were discussed somewhat superficially, and greater detail in many parts of the book would have been welcome.

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Book description

The JMP 13 Design of Experiments Guide covers classic DOE designs (for example, full factorial, response surface, and mixture designs). Read about more flexible custom designs, which you generate to fit your particular experimental situation. And discover JMP’s definitive screening designs, an efficient way to identify important factor interactions using fewer runs than required by traditional designs. The book also provides guidance on determining an appropriate sample size for your study.

Table of contents

• Documentation and Additional Resources
• Formatting Conventions
• JMP Documentation Library
• Sample Data Tables
• Learn about Statistical and JSL Terms
• Learn JMP Tips and Tricks
• JMP User Community
• JMPer Cable
• JMP Books by Users
• The JMP Starter Window
• Technical Support
• Overview of Design of Experiment Platforms
• Example and Key Concepts
• Overview of Experimental Design and the DOE Workflow
• Define the Study and Goals
• Define Responses and Factors
• Specify the Model
• Steps to Duplicate Results (Optional)
• Generate the Design
• Evaluate the Design
• Make the Table
• Run the Experiment
• Analyze the Data
• Effect Hierarchy
• Effect Heredity
• Effect Sparsity
• Center Points, Replicate Runs, and Testing
• Construct Designs That Meet Your Needs
• Overview of Custom Design
• Alias Terms
• Duplicate Results (Optional)
• Design Generation
• Design Evaluation
• Output Options
• Interpret the Full Model Results
• Reduce the Model
• Interpret the Reduced Model Results
• Optimize Factor Settings
• Lock a Factor Level
• Profiler with Rater
• Response Limits Column Property
• Factors Outline
• Factor Types
• Changes and Random Blocks
• Factor Column Properties
• Specify Linear Constraints
• Use Disallowed Combinations Filter
• Use Disallowed Combinations Script
• Description of Options
• Simulate Responses
• Save X Matrix
• Number of Starts
• Design Search Time
• Set Delta for Power
• Random Block Designs
• Split-Plot Designs
• Split-Split-Plot Designs
• Two-Way Split-Plot Designs
• Covariates with Hard-to-Change Levels
• Numbers of Whole Plots and Subplots
• D-Optimality
• Bayesian D-Optimality
• I-Optimality
• Bayesian I-Optimality
• Alias Optimality
• D-Efficiency
• Coordinate-Exchange Algorithm
• Perform Experiments That Meet Your Needs
• Design That Estimates Main Effects Only
• Design That Estimates All Two-Factor Interactions
• Design That Avoids Aliasing of Main Effects and Two-Factor Interactions
• Generate a Supersaturated Design
• Analyze a Supersaturated Design Using the Screening Platform
• Analyze a Supersaturated Design Using Stepwise Regression
• Design for Fixed Blocks
• Construct a Response Surface Design
• Analyze the Experimental Results
• Response Surface Design with Flexible Blocking
• I-Optimal Design
• D-Optimal Design
• Response Surface Design With Constraints and Categorical Factor
• Mixture Design with Nonmixture Factors
• Mixture of Mixtures Design
• Design with Fixed Covariates
• Design with Hard-to-Change Covariates
• Design with a Linear Time Trend
• Split-Plot Experiment
• Two-Way Split-Plot Experiment
• Analyze the Augmented Design
• Augment Design Launch Window
• Replicate a Design
• Add Center Points
• Creating a Foldover Design
• Adding Axial Points
• Space Filling
• Augment Design Options
• Overview of Definitive Screening Design
• Create the Design
• Comparison with a Fractional Factorial Design
• Analyze the Experimental Data
• Comparison of a Definitive Screening Design with a Plackett-Burman Design
• Blocking in Definitive Screening Designs
• Conference Matrices and the Number of Runs
• Definitive Screening Designs for Four or Fewer Factors
• Two-Way Interactions
• Forward Stepwise Regression or All Possible Subsets Regression
• Analyze Data from Definitive Screening Experiments
• Identification of Active Effects in DSDs
• Effective Model Selection for DSDs
• Fit the Model
• Examine Results
• Launch the Fit Definitive Screening Platform
• Stage 1 - Main Effect Estimates
• Stage 2 - Even Order Effect Estimates
• Combined Model Parameter Estimates
• Main Effects Plot
• Prediction Profiler
• Fit Definitive Screening Platform Options
• Decomposition of Response
• Stage 1 Methodology
• Stage 2 Methodology
• Underlying Principles
• Analysis of Screening Design Results
• Constructing a Standard Screening Design
• Specify the Response
• Specify Factors
• Constructing a Main Effects Screening Design
• Main Effects Screening Design where No Standard Design Exists
• Choose Screening Type
• Choose from a List of Fractional Factorial Designs
• Two-Level Full Factorial
• Two-Level Regular Fractional Factorial
• Plackett-Burman Designs
• Mixed-Level Designs
• Cotter Designs
• Resolution as a Measure of Confounding
• Change Generating Rules
• Chi-Square Efficiency
• Screening Design Options
• Create the Standard Fractional Factorial Design
• Change the Generating Rules to Obtain a Different Fraction
• Analyze the Results
• Plackett-Burman Design
• Analyze Data from Screening Experiments
• Overview of the Fit Two Level Screening Platform
• An Example Comparing Fit Two Level Screening and Fit Model
• Launch the Fit Two Level Screening Platform
• Half Normal Plot
• The Actual-by-Predicted Plot
• The Scaled Estimates Report
• A Power Analysis
• Analyzing a Plackett-Burman Design
• Analyzing a Supersaturated Design
• Order of Effect Entry
• Fit Two Level Screening as an Orthogonal Rotation
• Lenth’s Pseudo-Standard Error
• Lenth t-Ratios
• Overview of Response Surface Designs
• Construct a Box-Behnken Design
• Explore Optimal Settings
• Box-Behnken Designs
• Central Composite Designs
• Specify Output Options
• Response Surface Design Options
• Overview of Full Factorial Design
• Construct the Design
• Analysis Using Screening Platform
• Analysis Using Stepwise Regression
• Optimal Settings Using the Prediction Profiler
• Center Points and Replicates
• Design Table Scripts
• Pattern Column
• Full Factorial Design Options
• Overview of Mixture Designs
• Factors List
• Linear Constraints
• Examples of Mixture Design Types
• Adding Effects to the Model
• Creating the Design
• Simplex Centroid Design Examples
• Simplex Lattice Design
• An Extreme Vertices Example with Range Constraints
• An Extreme Vertices Example with Linear Constraints
• Extreme Vertices Method: How It Works
• ABCD Design
• FFF Optimality Criterion
• Set Average Cluster Size
• Space Filling Example
• A Space Filling Example with a Linear Constraint
• Creating Ternary Plots
• Whole Model Tests and Analysis of Variance Reports
• Understanding Response Surface Reports
• Analyze the Mixture Model
• The Prediction Profiler
• The Mixture Profiler
• A Ternary Plot of the Mixture Response Surface
• Overview of Taguchi Designs
• Example of a Taguchi Design
• Choose Inner and Outer Array Designs
• Display Coded Design
• Make the Design Table
• Explore Properties of Your Design
• Overview of Evaluate Design
• Construct the Intended and Actual Designs
• Comparison of Intended and Actual Designs
• Evaluating Power Relative to a Specified Model
• Evaluate Design Launch Window
• Power Analysis Overview
• Power Analysis Details
• Power Analysis for Coffee Experiment
• Prediction Variance Profile
• Fraction of Design Space Plot
• Prediction Variance Surface
• Fractional Increase in CI Length
• Relative Std Error of Estimate
• Alias Matrix Examples
• Color Map Example
• D Efficiency
• G Efficiency
• A Efficiency
• Average Variance of Prediction
• Design Creation Time
• Evaluate Design Options
• Compare and Evaluate Designs Simultaneously
• Overview of Comparing Designs
• Comparison in Terms of Main Effects Only
• Designs of Different Run Sizes
• Split Plot Designs with Different Numbers of Whole Plots
• Compare Designs Launch Window
• Reference Design
• Power Analysis Report
• Power versus Sample Size
• Relative Estimation Efficiency
• Relative Standard Error of Estimates
• Alias Matrix
• Example of Calculation of Alias Matrix Summary Values
• Absolute Correlations Table
• Color Map on Correlations
• Absolute Correlations and Color Map on Correlations Example
• Efficiency and Additional Run Size
• Relative Efficiency Measures
• Compare Designs Options
• Launching the Sample Size and Power Platform
• Power versus Sample Size Plot
• Power versus Difference Plot
• Sample Size and Power Animation for One Mean
• Plot of Power by Sample Size
• k-Sample Means
• One Sample Standard Deviation Example
• Actual Test Size
• One-Sample Proportion Window Specifications
• Two Sample Proportion Window Specifications
• Counts per Unit Example
• Sigma Quality Level Example
• Number of Defects Computation Example
• Create a Design for Selecting Preferred Product Profiles
• Choice Design Terminology
• Example of a Choice Design
• Define Factors and Levels
• Analyze the Pilot Study Data
• Design the Final Choice Experiment Using Prior Information
• Determine Significant Attributes
• Find Unit Cost and Trade Off Costs
• Attribute Column Properties
• DOE Model Controls
• Prior Specification
• Choice Design Options
• Bayesian D-Optimality and Design Construction
• Utility-Neutral and Local D-Optimal Designs
• Create a Design for Selecting Best and Worst Items
• MaxDiff Design Platform Overview
• Example of a MaxDiff Design
• MaxDiff Design Launch Window
• Design Options Outline
• Design Outline
• MaxDiff Options
• Detecting Component Interaction Failures
• Overview of Covering Arrays
• Load Factors
• Restrict Factor Level Combinations
• Specify Disallowed Combinations Using the Filter
• Specify Disallowed Combinations Using a Script
• Construct the Design Table
• Factors Table
• Editing the Factors Table
• Unsatisfiable Constraints
• Analysis Script
• Covering Array Options
• Algorithm for Optimize
• Unconstrained Design
• Constrained Design
• Overview of Space-Filling Designs
• Space Filling Design Methods
• Design Diagnostics
• Design Table
• Space Filling Design Options
• Creating a Sphere-Packing Design
• Visualizing the Sphere-Packing Design
• Creating a Latin Hypercube Design
• Visualizing the Latin Hypercube Design
• Uniform Designs
• Comparing Sphere-Packing, Latin Hypercube, and Uniform Methods
• Minimum Potential Designs
• Maximum Entropy Designs
• Gaussian Process IMSE Optimal Designs
• Categorical Factors
• Constraints
• Creating and Viewing a Constrained Fast Flexible Filling Design
• Create the Sphere-Packing Design for the Borehole Data
• Results of the Borehole Experiment
• Designing Experiments for Accelerated Life Tests
• Overview of Accelerated Life Test Designs
• Obtain Prior Estimates
• Enter Basic Specifications
• Enter Prior Information and Remaining Specifications
• Example of Augmenting an Accelerated Life Test Design
• Specify the Design Structure
• Specify Acceleration Factors
• Specify Design Details
• Review Balanced Design Diagnostics and Update Specifications
• Create and Assess the Optimal Design
• Update the Design and Create Design Tables
• Platform Options
• Overview of Nonlinear Designs
• Explore the Design
• Obtain Prior Parameter Estimates
• Augment the Design
• View the Design
• Nonlinear Design Launch Window
• Make Table or Augment Table
• Nonlinear Design Options
• Nonlinear Models
• Radial-Spherical Integration of the Optimality Criterion
• Finding the Optimal Design
• Understanding Column Properties Assigned by DOE
• Adding and Viewing Column Properties
• Response Limits Example
• Editing Response Limits
• Design Role Example
• Low and High Values
• Coding Column Property and Center Polynomials
• Coding Example
• Assigning Coding
• Mixture Example
• Factor Changes Example
• Value Ordering Example
• Assigning Value Ordering
• Value Labels Example
• RunsPerBlock Example
• ConstraintState Example
• Designs with Hard or Very Hard Factor Changes
• Designs with If Possible Effects
• Power for a Single Parameter
• Power for a Categorical Effect
• Relative Prediction Variance
• Design of Experiments Guide

Product information

• Title: JMP 13 Design of Experiments Guide
• Author(s): SAS Institute
• Release date: September 2016
• Publisher(s): SAS Institute
• ISBN: 9781629605623

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